On the boundary value problem for functional differential inclusion of fractional order with common initial condition on a Banach space

We consider the problem for a functional differential inclusion of fractional order with a general initial condition expressed in the form of an operator inclusion in a Banach space. At the beginning of the article, an introduction is presented in which the relevance of the study is substantiated, then preliminary information from fractional analysis, the theory of measures of noncompactness and condensing mappings, as well as some information from a multivalued analysis are given. In the second subsection we state the problem and its solution on the basis of the theory of condensing multivalued mappings. In the last subsection we give an example of a particular case of the solved problem, in the case of an antiperiodic boundary condition.